Transmitter diversity technique for wireless communications

ABSTRACT

A simple block coding arrangement is created with symbols transmitted over a plurality of transmit channels, in connection with coding that comprises only simple arithmetic operations, such as negation and conjugation. The diversity created by the transmitter utilizes space diversity and either time or frequency diversity. Space diversity is effected by redundantly transmitting over a plurality of antennas, time diversity is effected by redundantly transmitting at different times, and frequency diversity is effected by redundantly transmitting at different frequencies: Illustratively, using two transmit antennas and a single receive antenna, one of the disclosed embodiments provides the same diversity gain as the maximal-ratio receiver combining (MRRC) scheme with one transmit antenna and two receive antennas. The principles of this invention are applicable to arrangements with more than two antennas, and an illustrative embodiment is disclosed using the same space block code with two transmit and two receive antennas.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a division of U.S. application Ser. No. 13/073,369,filed Mar. 28, 2011 (now U.S. Pat. No. 8,355,475), which is acontinuation of U.S. application Ser. No. 11/828,790, filed Jul. 26,2007 (now U.S. Pat. No. 7,916,806), which is a division of U.S.application Ser. No. 11/536,474, filed Sep. 28, 2006 (now U.S. Pat. No.7,386,077), which is a continuation of U.S. application Ser. No.10/873,567, filed Jun. 22, 2004 (now U.S. Pat. No. 7,120,200), which isa continuation of U.S. application Ser. No. 09/730,151, filed Dec. 5,2000 (now U.S. Pat. No. 6,775,329), which is a continuation of U.S.application Ser. No. 09/074,224, filed May 7, 1998 (now U.S. Pat. No.6,185,258), which claims the benefit of U.S. Provisional Application No.60/059,016, filed Sep. 16, 1997, U.S. Provisional Application No.60/059,219, filed Sep. 18, 1997, and U.S. Provisional Application No.60/063,780, filed Oct. 31, 1997; all of which applications are herebyincorporated by reference herein in their entirety.

BACKGROUND OF THE INVENTION

This invention relates to wireless communication and, more particularly,to techniques for effective wireless communication in the presence offading and other degradations.

The most effective technique for mitigating multipath fading in awireless radio channel is to cancel the effect of fading at thetransmitter by controlling the transmitter's power. That is, if thechannel conditions are known at the transmitter (on one side of thelink), then the transmitter can pre-distort the signal to overcome theeffect of the channel at the receiver (on the other side). However,there are two fundamental problems with this approach. The first problemis the transmitter's dynamic range. For the transmitter to overcome an xdB fade, it must increase its power by x dB which, in most cases, is notpractical because of radiation power limitations, and the size and costof amplifiers. The second problem is that the transmitter does not haveany knowledge of the channel as seen by the receiver (except for timedivision duplex systems, where the transmitter receives power from aknown other transmitter over the same channel). Therefore, if one wantsto control a transmitter based on channel characteristics, channelinformation has to be sent from the receiver to the transmitter, whichresults in throughput degradation and added complexity to both thetransmitter and the receiver.

Other effective techniques are time and frequency diversity. Using timeinterleaving together with coding can provide diversity improvement. Thesame holds for frequency hopping and spread spectrum. However, timeinterleaving results in unnecessarily large delays when the channel isslowly varying. Equivalently, frequency diversity techniques areineffective when the coherence bandwidth of the channel is large (smalldelay spread).

It is well known that in most scattering environments antenna diversityis the most practical and effective technique for reducing the effect ofmultipath fading. The classical approach to antenna diversity is to usemultiple antennas at the receiver and perform combining (or selection)to improve the quality of the received signal.

The major problem with using the receiver diversity approach in currentwireless communication systems, such as IS-136 and GSM, is the cost,size and power consumption constraints of the receivers. For obviousreasons, small size, weight and cost are paramount. The addition ofmultiple antennas and RF chains (or selection and switching circuits) inreceivers is presently not feasible. As a result, diversity techniqueshave often been applied only to improve the up-link (receiver to base)transmission quality with multiple antennas (and receivers) at the basestation. Since a base station often serves thousands of receivers, it ismore economical to add equipment to base stations rather than thereceivers.

Recently, some interesting approaches for transmitter diversity havebeen suggested. A delay diversity scheme was proposed by A. Wittneben in“Base Station Modulation Diversity for Digital SIMULCAST,” Proceedingsof the 1991 IEEE Vehicular Technology Conference (VTC 41 st), pp.848-853, May 1991, and in “A New Bandwidth Efficient Transmit AntennaModulation Diversity Scheme For Linear Digital Modulation,” inProceedings of the 1993 IEEE International Conference on Communications(IICC '93), pp. 1630-1634, May 1993. The proposal is for a base stationto transmit a sequence of symbols through one antenna, and the samesequence of symbols—but delayed—through another antenna.

U.S. Pat. No. 5,479,448, issued to Nambirajan Seshadri on Dec. 26, 1995,discloses a similar arrangement where a sequence of codes is transmittedthrough two antennas. The sequence of codes is routed through a cyclingswitch that directs each code to the various antennas, in succession.Since copies of the same symbol are transmitted through multipleantennas at different times, both space and time diversity are achieved.A maximum likelihood sequence estimator (MLSE) or a minimum mean squarederror (MMSE) equalizer is then used to resolve multipath distortion andprovide diversity gain. See also N. Seshadri, J. H. Winters, “TwoSignaling Schemes for Improving the Error Performance of FDDTransmission Systems Using Transmitter Antenna Diversity,” Proceedingsof the 1993 IEEE Vehicular Technology Conference (VTC 43rd), pp.508-511, May 1993; and J. H. Winters, “The Diversity Gain of TransmitDiversity in Wireless Systems with Rayleigh Fading,” Proceedings of the1994 ICC/SUPERCOMM, New Orleans, Vol. 2, pp. 1121-1125, May 1994.

Still another interesting approach is disclosed by Tarokh, Seshadri,Calderbank and Naguib in U.S. application, Ser. No. 08/847,635, filedApr. 25, 1997 (based on a provisional application filed Nov. 7, 1996),where symbols are encoded according to the antennas through which theyare simultaneously transmitted, and are decoded using a maximumlikelihood decoder. More specifically, the process at the transmitterhandles the information in blocks of M1 bits, where M1 is a multiple ofM2, i.e., M1=k*M2. It converts each successive group of M2 bits intoinformation symbols (generating thereby k information symbols), encodeseach sequence of k information symbols into n channel codes (developingthereby a group of n channel codes for each sequence of k informationsymbols), and applies each code of a group of codes to a differentantenna.

SUMMARY

The problems of prior art systems are overcome, and an advance in theart is realized with a simple block coding arrangement where symbols aretransmitted over a plurality of transmit channels and the codingcomprises only simple arithmetic operations, such as negation andconjugation. The diversity created by the transmitter utilizes spacediversity and either time diversity or frequency diversity. Spacediversity is effected by redundantly transmitting over a plurality ofantennas; time diversity is effected by redundantly transmitting atdifferent times; and frequency diversity is effected by redundantlytransmitting at different frequencies. Illustratively, using twotransmit antennas and a single receive antenna, one of the disclosedembodiments provides the same diversity gain as the maximal-ratioreceiver combining (MRRC) scheme with one transmit antenna and tworeceive antennas. The novel approach does not require any bandwidthexpansion or feedback from the receiver to the transmitter, and has thesame decoding complexity as the MRRC. The diversity improvement is equalto applying maximal-ratio receiver combining (MRRC) at the receiver withthe same number of antennas. The principles of this invention areapplicable to arrangements with more than two antennas, and anillustrative embodiment is disclosed using the same space block codewith two transmit and two receive antennas. This scheme provides thesame diversity gain as four-branch MRRC.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a first embodiment in accordance with theprinciples of this invention;

FIG. 2 presents a block diagram of a second embodiment, where channelestimates are not employed;

FIG. 3 shows a block diagram of a third embodiment, where channelestimates are derived from recovered signals; and

FIG. 4 illustrates an embodiment where two transmitter antennas and tworeceiver antennas are employed.

DETAILED DESCRIPTION

In accordance with the principles of this invention, effectivecommunication is achieved with encoding of symbols that comprises merelynegations and conjugations of symbols (which really is merely negationof the imaginary part) in combination with a transmitter createddiversity. Space diversity and either frequency diversity or timediversity are employed.

FIG. 1 presents a block diagram of an arrangement where the twocontrollable aspects of the transmitter that are used are space andtime. That is, the FIG. 1 arrangement includes multiple transmitterantennas (providing space diversity) and employs multiple timeintervals. Specifically, transmitter 10 illustratively comprisesantennas 11 and 12, and it handles incoming data in blocks of n symbols,where n is the number of transmitter antennas, and in the illustrativeembodiment of FIG. 1, it equals 2, and each block takes n symbolintervals to transmit. Also illustratively, the FIG. 1 arrangementincludes a receiver 20 that comprises a single antenna 21.

At any given time, a signal sent by a transmitter antenna experiencesinterference effects of the traversed channel, which consists of thetransmit chain, the air-link, and the receive chain. The channel may bemodeled by a complex multiplicative distortion factor composed of amagnitude response and a phase response. In the exposition that followstherefore, the channel transfer function from transmit antenna 11 toreceive antenna 21 is denoted by h₀ and from transmit antenna 12 toreceive antenna 21 is denoted by h₁ where:h ₀=α₀ e ^(jθ) ⁰h ₁=α₁ e ^(jθ) ¹   (1)Noise from interference and other sources is added at the two receivedsignals and, therefore, the resulting baseband signal received at anytime and outputted by reception and amplification section 25 isr(t)=α₀ e ^(jθ) ⁰ s _(i)+α₁ e ^(jθ) ¹ s _(j) +n(t),  (2)where s_(i) and s_(j) are the signals being sent by transmit antenna 11and 12, respectively.

As indicated above, in the two-antenna embodiment of FIG. 1 each blockcomprises two symbols and it takes two symbol intervals to transmitthose two symbols. More specifically, when symbols s_(i) and s_(j) needto be transmitted, at a first time interval the transmitter appliessignal s_(i) to antenna 11 and signal s_(j) to antenna 12, and at thenext time interval the transmitter applies signal −s_(j)*; to antenna 11and signal s_(j)* to antenna 12. This is clearly a very simple encodingprocess where only negations and conjugations are employed. Asdemonstrated below, it is as effective as it is simple. Corresponding tothe above-described transmissions, in the first time interval thereceived signal isr(t)=h ₀ s _(i) +h ₁ s _(j) +n(t),  (3)and in the next time interval the received signal isr(t+T)=−h ₀ s _(j) *+h ₁ s _(i) *+n(t+T).  (4)

Table 1 illustrates the transmission pattern over the two antennas ofthe FIG. 1 arrangement for a sequence of signals {s₀, s₁, s₂, s₃, s₄, s₅. . . }.

TABLE 1 Time: t t + T t + 2T t + 3T t + 4T t + 5T Antenna 11 s₀ −s₁* s₂−s₃* s₄ −s₅* . . . Antenna 12 s₁ s₀* s₃ s₂* s₅ s₄* . . .

The received signal is applied to channel estimator 22, which providessignals representing the channel characteristics or, rather, the bestestimates thereof. Those signals are applied to combiner 23 and tomaximum likelihood detector 24. The estimates developed by channelestimator 22 can be obtained by sending a known training signal thatchannel estimator 22 recovers, and based on the recovered signal thechannel estimates are computed. This is a well known approach.

Combiner 23 receives the signal in the first time interval, buffers it,receives the signal in the next time interval, and combines the tworeceived signals to develop signals{tilde over (s)} _(i) ={tilde over (h)} ₀ *r(t)+{tilde over (h)} ₁r*(t+T){tilde over (s)} _(j) ={tilde over (h)} ₁ *r(t)−{tilde over (h)} ₀r*(t+T)  (5)Substituting equation (1) into (5) yields{tilde over (s)} _(i)=({tilde over (α)}₀ ²+{tilde over (α)}₁ ²)s _(i)+{tilde over (h)} ₀ *n(t)+{tilde over (h)} ₁ n*(t+T){tilde over (s)} _(j)=({tilde over (α)}₀ ²+{tilde over (α)}₁ ²)s _(j)+{tilde over (h)} ₀ n*(t+T)+{tilde over (h)} ₁ *n(t),  (6)where {tilde over (α)}₀ ²={tilde over (h)}₀{tilde over (h)}₀* and {tildeover (α)}₁ ²={tilde over (h)}₁{tilde over (h)}₁*, demonstrating that thesignals of equation (6) are, indeed, estimates of the transmittedsignals (within a multiplicative factor). Accordingly, the signals ofequation (6) are sent to maximum likelihood detector 24.

In attempting to recover s_(i), two kinds of signals are considered: thesignals actually received at time t and t+T, and the signals that shouldhave been received if s_(i) were the signal that was sent. Asdemonstrated below, no assumption is made regarding the value of Thatis, a decision is made that s_(i)=s_(x) for that value of x for whichd ² [r(t),(h ₀ s _(x) +h ₁ s _(j))]+d ² [r(t+T),(−h ₁ s _(j) *+h ₀ s_(x)*)]is less thand ² [r(t),(h ₀ s _(k) +h ₁ s _(j))]+d ² [r(t+T),(−h ₁ s _(j) *+h ₀ s_(k)*)]  (7)where d² (x, y) is the squared Euclidean distance between signals x andy, i.e., d² (x, y)=|x−y|².

Recognizing that {tilde over (h)}₀=h₀+noise that is independent of thetransmitted symbol, and that {tilde over (h)}₁=h₁+noise that isindependent of the transmitted symbol, equation (7) can be rewritten toyield(α₀ ²+α₁ ²)|s _(x)|² −{tilde over (s)} _(i) s _(x) *−{tilde over (s)}_(i) *s _(x)≦(α₀ ²+α₁ ²)|s _(k)|² −{tilde over (s)} _(i) s _(k) *−{tildeover (s)} _(i) *s _(k)  (8)where α₀ ²=h₀h₀* and α₁ ²=h₁h₁*; or equivalently(α₀ ²+α₁ ²−1)|s _(x)|² +d ²({tilde over (s)} _(i) ,s _(x))≦(α₀ ²+α₁²−1)|s _(k)|² +d ²({tilde over (s)} _(i) ,s _(k))  (9)

In Phase Shift Keying modulation, all symbols carry the same energy,which means that |s_(x)|²=|s_(k)|² and, therefore, the decision rule ofequation (9) may be simplified to choose signalŝ_(i)=s_(x) iff d ²({tilde over (s)} _(i) ,s _(x))≦d ²({tilde over (s)}_(i) ,s _(k)).  (10)Thus, maximum likelihood detector 24 develops the signals s_(k) for allvalues of k, with the aid of {tilde over (h)}₀ and {tilde over (h)}₁from estimator 22, develops the distances d²({tilde over (s)}_(i),s_(k)), identifies x for which equation (10) holds and concludes thatŝ_(i)=s_(x). A similar process is applied for recovering ŝ_(j).

In the above-described embodiment each block of symbols is recovered asa block with the aid of channel estimates {tilde over (h)}₀ and {tildeover (h)}₁. However, other approaches to recovering the transmittedsignals can also be employed. Indeed, an embodiment for recovering thetransmitted symbols exists where the channel transfer functions need notbe estimated at all, provided an initial pair of transmitted signals isknown to the receiver (for example, when the initial pair of transmittedsignals is prearranged). Such an embodiment is shown in FIG. 2, wheremaximum likelihood detector 27 is responsive solely to combiner 26.(Elements in FIG. 3 that are referenced by numbers that are the same asreference numbers in FIG. 1 are like elements.) Combiner 26 of receiver30 develops the signalsr ₀ =r(t)=h ₀ s ₀ +h ₁ s ₁ +n ₀r ₁ =r(t+T)=h ₁ s ₀ *−h ₀ s ₁ *+n ₁r ₂ =r(t+2T)=h ₀ s ₂ +h ₁ s ₃ +n ₂r ₃ =r(t+3T)=h ₁ s ₂ *−h ₀ s ₃ *+n ₃,  (11)then develops intermediate signals A and BA=r ₀ r ₃ *−r ₂ r _(i)*B=r ₂ r ₀ *−r ₁ r ₃*,  (12)and finally develops signals{tilde over (s)} ₂ =As ₁ *+Bs ₀{tilde over (s)} ₃ =−As ₀ *+Bs ₁,  (13)where N₃ and N₄ are noise terms. It may be noted that signal r₂ isactually r₂=h₀ŝ₂+h₁ŝ₃=h₀s₂+h₁s₃+n₂, and similarly for signal r₃. Sincethe makeup of signals A and B makes them also equal toA=(α₀ ²+α₁ ²)(s ₂ s ₁ −s ₃ s ₀)+N ₁B=(α₀ ²+α₁ ²)(s ₂ s ₀ *+s ₃ s ₁*)+N ₂,  (14)where N1 and N2 are noise terms, it follows that signals {tilde over(s)}₂ and {tilde over (s)}₃ are equal to{tilde over (s)} ₂=(α₀ ²+α₁ ²)(|s ₀|² +|s ₁|²)s ₂ +N ₃{tilde over (s)} ₃=(α₀ ²+α₁ ²)(|s ₀|² +|s ₁|²)(s ₃ +N ₄.  (15)

When the power of all signals is constant (and normalized to 1) equation(15) reduces to{tilde over (s)} ₂=(α₀ ²+α₁ ²)s ₂ +N ₃{tilde over (s)} ₃=(α₀ ²+α₁ ²)s ₃ +N ₄.  (16)

Hence, signals {tilde over (s)}₂ and {tilde over (s)}₃ are, indeed,estimates of the signals s₂ and s₃ (within a multiplicative factor).Lines 28 and 29 demonstrate the recursive aspect of equation (13), wheresignal estimates {tilde over (s)}₂ and {tilde over (s)}₃ are evaluatedwith the aid of recovered signals s₀ and s₁ that are fed back from theoutput of the maximum likelihood detector.

Signals {tilde over (s)}₂ and {tilde over (s)}₃ are applied to maximumlikelihood detector 24 where recovery is effected with the metricexpressed by equation (10) above. As shown in FIG. 2, once signals s₂and s₃ are recovered, they are used together with received signals r₂,r₃, r₄, and r₅ to recover signals s₄ and s₅, and the process repeats.

FIG. 3 depicts an embodiment that does not require the constellation ofthe transmitted signals to comprise symbols of equal power. (Elements inFIG. 3 that are referenced by numbers that are the same as referencenumbers in FIG. 1 are like elements.) In FIG. 3, channel estimator 43 ofreceiver 40 is responsive to the output signals of maximum likelihooddetector 42. Having access to the recovered signals s₀ and s₁, channelestimator 43 forms the estimates

$\begin{matrix}{{{\overset{\sim}{h}}_{0} = {\frac{{r_{0}s_{0}^{*}} - {r_{1}s_{1}}}{{s_{0}}^{2} + {s_{1}}^{2}} = {h_{0} + \frac{{s_{0}^{*}n_{0}} + {s_{1}n_{1}}}{{s_{0}}^{2} + {s_{1}}^{2}}}}}{{\overset{\sim}{h}}_{1} = {\frac{{r_{0}s_{1}^{*}} - {r_{1}s_{0}}}{{s_{0}}^{2} + {s_{1}}^{2}} = {h_{1} + \frac{{s_{1}^{*}n_{0}} + {s_{0}n_{1}}}{{s_{0}}^{2} + {s_{1}}^{2}}}}}} & (17)\end{matrix}$and applies those estimates to combiner 23 and to detector 42. Detector24 recovers signals s₂ and s₃ by employing the approach used by detector24 of FIG. 1, except that it does not employ the simplification ofequation (9). The recovered signals of detector 42 are fed back tochannel estimator 43, which updates the channel estimates in preparationfor the next cycle.

The FIGS. 1-3 embodiments illustrate the principles of this inventionfor arrangements having two transmit antennas and one receive antenna.However, those principles are broad enough to encompass a plurality oftransmit antennas and a plurality of receive antennas. To illustrate,FIG. 4 presents an embodiment where two transmit antennas and tworeceive antennas are used; to wit, transmit antennas 31 and 32, andreceive antennas 51 and 52. The signal received by antenna 51 is appliedto channel estimator 53 and to combiner 55, and the signal received byantenna 52 is applied to channel estimator 54 and to combiner 55.Estimates of the channel transfer functions h₀ and h₁ are applied bychannel estimator 53 to combiner 55 and to maximum likelihood detector56. Similarly, estimates of the channel transfer functions h₂ and h₃ areapplied by channel estimator 54 to combiner 55 and to maximum likelihooddetector 56. Table 2 defines the channels between the transmit antennasand the receive antennas, and table 3 defines the notion for thereceived signals at the two receive antennas.

TABLE 2 Antenna 51 Antenna 52 Antenna 31 h₀ h₂ Antenna 32 h₁ h₃

TABLE 3 Antenna 51 Antenna 52 Time t r₀ r₂ Time t + T r₁ r₃

Based on the above, it can be shown that the received signals arer ₀ =h ₀ s ₀ +h ₁ s ₁ +n ₀r ₁ =−h ₀ s ₁ *+h ₁ s ₀ *+n ₁r ₂ =h ₂ s ₀ +h ₃ s ₁ +n ₂r ₃ =−h ₂ s ₁ *+h ₃ s ₀ *+n ₃  (18)where n₀, n₁, n₂, and n₃ are complex random variables representingreceiver thermal noise, interferences, etc.

In the FIG. 4 arrangement, combiner 55 develops the following twosignals that are sent to the maximum likelihood detector:{tilde over (s)} ₀ =h ₀ *r ₀ h ₁ r ₁ *+h ₂ *r ₂ +h ₃ r ₃*{tilde over (s)} ₁ =h ₁ *r ₀ −h ₀ r ₁ *+h ₃ *r ₂ −h ₂ r ₃.*  (19)

Substituting the appropriate equations results in{tilde over (s)} ₀=(α₀ ²+α₁ ²+α₂ ²+α₃ ²)s ₀ +h ₀ *n ₀ +h ₁ n ₁ *+h ₂ *n₂ +h ₃ n ₃*{tilde over (s)} ₁=(α₀ ²+α₁ ²+α₂ ²+α₃ ²)s ₁ +h ₁ *n ₀ −h ₀ n ₁ *+h ₃ *n₂ −h ₂ n ₃*  (20)which demonstrates that the signal {tilde over (s)}₀ and {tilde over(s)}₁ are indeed estimates of the signals s₀ and s₁. Accordingly,signals {tilde over (s)}₀ and {tilde over (s)}₁ are sent to maximumlikelihood decoder 56, which uses the decision rule of equation (10) torecover the signals ŝ₀ and ŝ₁.

As disclosed above, the principles of this invention rely on thetransmitter to force a diversity in the signals received by a receiver,and that diversity can be effected in a number of ways. The illustratedembodiments rely on space diversity—effected through a multiplicity oftransmitter antennas, and time diversity—effected through use of twotime intervals for transmitting the encoded symbols. It should berealized that two different transmission frequencies could be usedinstead of two time intervals. Such an embodiment would double thetransmission speed, but it would also increase the hardware in thereceiver, because two different frequencies need to be received andprocessed simultaneously.

The above illustrated embodiments are, obviously, merely illustrativeimplementations of the principles of the invention, and variousmodifications and enhancements can be introduced by artisans withoutdeparting from the spirit and scope of this invention, which is embodiedin the following claims. For example, all of the disclosed embodimentsare illustrated for a space-time diversity choice, but as explainedabove, one could choose the space-frequency pair. Such a choice wouldhave a direct effect on the construction of the receivers.

The invention claimed is:
 1. A method comprising: receiving first andsecond symbols at an encoder; encoding the received first and secondsymbols, the encoding including generating a complex conjugate of thefirst symbol and generating a negative complex conjugate of the secondsymbol; transmitting the first symbol and the complex conjugate of thefirst signal with space diversity; and transmitting the second symboland negative complex conjugate of the second symbol with spacediversity.
 2. The method as recited in claim 1 further comprisingtransmitting the first symbol and the complex conjugate of the firstsignal with frequency diversity.
 3. The method as recited in claim 2further comprising transmitting the second symbol and the negativecomplex conjugate of the second signal with frequency diversity.
 4. Themethod as recited in claim 3 further comprising: transmitting the firstsymbol and the negative complex conjugate of the second symbol over afirst antenna; and transmitting the second symbol and the complexconjugate of the first symbol over a second antenna.
 5. The method asrecited in claim 1 further comprising transmitting the first symbol andthe complex conjugate of the first signal with time diversity.
 6. Themethod as recited in claim 5 further comprising transmitting the secondsymbol and the negative complex conjugate of the second signal with timediversity.
 7. The method as recited in claim 6 further comprising:transmitting the first symbol and the negative complex conjugate of thesecond symbol over a first antenna; and transmitting the second symboland the complex conjugate of the first symbol over a second antenna. 8.A transmitter apparatus comprising: a coder responsive to incoming firstand second symbols to form encoded sets of symbols, each of the encodedsets of symbols including an incoming symbol and a related symbol, therelated symbol being a complex conjugate or a negative complex conjugateof the incoming symbol, wherein the related symbol for the firstincoming symbol is a complex conjugate of the first incoming symbol andthe related symbol for the second incoming symbol is a negative complexconjugate of the second incoming symbol; and an output stage to apply,for each encoded set, the incoming symbol and the related symbol todifferent transmit antennas to transmit the encoded set with spacediversity, the encoded set being further transmitted with one offrequency diversity or time diversity.